Stability Analysis for the Non-Linear Model Predictive Control of a Flexible Joint Manipulator with Dynamics Uncertainties

Abstract

In this research, the problem of controlling a one-link robot with joint flexibility by the non-linear model predictive control method (NMPC) is considered. The issue concerning the input-to-state stability (ISS) of the NMPC has been considered. Through using the cost function of the NMPC problem in order to play the role of the Lyapunov function, the ISS stability of the system in the presence of disturbances and uncertainties, such as robot joint flexibility, is reached. Two modeling examples for a single-link robot have been investigated, which include unmeasurable variables as a portion of the system state variables. These unmeasured states are representative of the unmodeled dynamics, standing for either the flexibility at the joint or the link itself. In the first example, the control input is the actuation torque, and in the second one, the voltage to the motor. Simulation results demonstrate the effectiveness and stability of the proposed approach in the presence of disturbances and system uncertainties. © 2023 IEEE.